1 Introduction and dataset

We analyze one-minute disdrometric data recorded by two Thies LPM and two Parsivel2 disdrometers at the Aula Dei Experimental Station (41º43’30”N, 0º48’39”W, 230 m.a.s.l.), between 2013-06-17 and 2015-07-21. The disdrometers where installed on two masts with a separation of 1.5 m between them (Figure 1).

Fig 1. Experimental setup.

A total of 510 events were recorded during that period, spanning between 5 and 1454 minutes. This sums up to ~75k to ~99k one-minute records, depending on the device (see main article, Table 3).

The dataset analysed here corresponds to the common minutes, defined as those having high quality data and detection of rainfall particles in each of the four disdrometers (see main article, secion 2.3). This led to a total of 46,636 records, corresponding to 11,659 minutes belonging to 157 rainfall episodes.

We shall start by reading and formatting the dataset. There are two alternative datasets: * file ./data/data.csv.gz, with variables as measured by devices and calculated from the particle size and velocity (PSVD) data, after a filtering and correction procedure was applied to the raw PSVD data to remove ulikely particle size and velocity bins (see main article, section 2.2); * file ./data/data_unfiltered.csv.gz, as the previous one but using the raw PSVD data (i.e., with no filtering and correction).

The first dataset will be stored in object ‘dat’, while the second dataset will be stored in object ‘datunf’.

# load data (filtered dataset)
dat <- read.table('./data/data.csv.gz', sep=',', head=TRUE)

# format factors
dat$Event <- as.factor(dat$Event)
dat$ID <- factor(dat$ID, levels=c('T1','T2','P1','P2'))
dat$Type <- factor(dat$Type)

# format time
dat$Time <- strptime(dat$Time, format='%Y-%m-%d %H:%M:%S')

head(dat)
##                  Time Event ID Serial Type Mast NP_meas R_meas Z_meas
## 1 2013-06-17 11:42:00     2 T1    436  Thi    1     121  1.400   30.8
## 2 2013-06-17 11:43:00     2 T1    436  Thi    1      96  0.921   27.1
## 3 2013-06-17 11:56:00     2 T1    436  Thi    1      26  0.275   20.7
## 4 2013-06-17 23:31:00     3 T1    436  Thi    1      27  0.330   20.8
## 5 2013-06-17 23:32:00     3 T1    436  Thi    1      29  0.355   21.3
## 6 2013-06-17 23:33:00     3 T1    436  Thi    1      47  0.506   22.4
##   E_meas  Pcum_meas Ecum_meas NP       ND      R        P     Z M     E
## 1     NA 0.02333333        NA 71 7265.362 1.3860 0.023110 31.49 0 22.07
## 2     NA 0.03868333        NA 69 6871.656 0.9138 0.015230 27.06 0 16.59
## 3     NA 0.04326667        NA 22 6480.489 0.3137 0.005228 22.16 0 14.96
## 4     NA 0.04876667        NA 21 3602.272 0.3440 0.005733 21.17 0 13.43
## 5     NA 0.05468333        NA 26 4801.632 0.3595 0.005992 21.63 0 14.20
## 6     NA 0.06311667        NA 38 3996.339 0.5613 0.009355 23.93 0 13.54
##         Pcum      Ecum   D10   D25   D50   D75   D90    Dm   V10   V25
## 1 0.02310000 0.3678333 0.262 0.296 0.351 0.657 1.496 0.858 0.871 0.996
## 2 0.03833000 0.6443333 0.321 0.366 0.886 1.239 1.408 0.990 1.035 1.303
## 3 0.04355833 0.8936667 0.318 0.334 0.684 1.133 1.343 0.986 1.140 1.316
## 4 0.04929167 1.1175000 0.370 0.692 1.026 1.369 1.492 1.195 1.386 4.146
## 5 0.05528333 1.3541667 0.294 0.701 1.089 1.173 1.260 1.113 1.329 3.390
## 6 0.06463833 1.5798333 0.341 0.793 1.038 1.143 1.280 1.162 1.555 3.320
##     V50   V75   V90    Vm
## 1 1.284 4.153 4.983 2.795
## 2 3.937 4.581 4.960 3.602
## 3 3.448 4.252 5.007 3.663
## 4 4.384 4.720 4.990 4.516
## 5 3.816 4.200 4.600 4.075
## 6 3.828 4.549 4.873 4.233
# load data (unfiltered dataset)
datunf <- read.table('./data/data_unfiltered.csv.gz', sep=',', head=TRUE)

# format factors
datunf$Event <- as.factor(datunf$Event)
datunf$ID <- factor(datunf$ID, levels=c('T1','T2','P1','P2'))
datunf$Type <- factor(datunf$Type)

# format time
datunf$Time <- strptime(datunf$Time, format='%Y-%m-%d %H:%M:%S')

head(datunf)
##                  Time Event ID Serial Type Mast NP_meas R_meas Z_meas
## 1 2013-06-17 11:42:00     2 T1    436  Thi    1     121  1.400   30.8
## 2 2013-06-17 11:43:00     2 T1    436  Thi    1      96  0.921   27.1
## 3 2013-06-17 11:56:00     2 T1    436  Thi    1      26  0.275   20.7
## 4 2013-06-17 23:31:00     3 T1    436  Thi    1      27  0.330   20.8
## 5 2013-06-17 23:32:00     3 T1    436  Thi    1      29  0.355   21.3
## 6 2013-06-17 23:33:00     3 T1    436  Thi    1      47  0.506   22.4
##   E_meas  Pcum_meas Ecum_meas  NP        ND      R        P     Z M     E
## 1     NA 0.02333333        NA 121 17439.908 1.3130 0.021880 31.22 0 21.94
## 2     NA 0.03868333        NA  96 16015.665 0.8768 0.014610 26.82 0 16.45
## 3     NA 0.04326667        NA  26  9505.014 0.3006 0.005011 21.95 0 14.92
## 4     NA 0.04876667        NA  27  5673.157 0.3338 0.005563 21.00 0 13.41
## 5     NA 0.05468333        NA  29  6203.553 0.3461 0.005769 21.43 0 14.12
## 6     NA 0.06311667        NA  47  7900.304 0.5408 0.009013 23.73 0 13.48
##         Pcum      Ecum   D10   D25   D50   D75   D90    Dm   V10   V25
## 1 0.02188333 0.3656667 0.167 0.212 0.298 0.373 1.846 0.574 0.671 0.881
## 2 0.03649667 0.6398333 0.181 0.249 0.452 1.231 1.515 0.756 0.596 1.046
## 3 0.04150667 0.8885000 0.210 0.296 0.587 1.378 1.632 0.856 1.016 1.110
## 4 0.04707000 1.1120000 0.307 0.455 1.085 1.525 1.637 1.007 1.159 3.807
## 5 0.05283833 1.3473333 0.296 0.622 1.142 1.342 1.525 1.017 1.117 3.489
## 6 0.06185167 1.5720000 0.166 0.362 1.063 1.354 1.587 0.961 0.959 3.279
##     V50   V75   V90    Vm
## 1 1.152 2.008 5.235 2.061
## 2 3.356 4.500 5.648 2.878
## 3 3.856 5.056 5.684 3.246
## 4 4.424 5.082 5.795 4.322
## 5 4.037 4.582 5.546 3.893
## 6 4.100 4.698 5.492 3.777

These are the variables included in the datasets:

var full name units
Time time of the record Y-m-d hh:mm:ss
Event event ID (factor)
ID disdromter ID (factor: T1, T2, P1, P2)
Serial disdrometer serial number (factor)
Type disdrometer type (factor: Thi, Par)
Mast mast ID (factor: 1, 2)
NP_meas number of particles detected (-)
R_meas rainfall intensity, as outputted by the device \(mm\ h^{-1}\)
Z_meas radar reflectivity, as outputted by the device \(dB\ mm^6\ m^{-3}\)
E_meas erosivity, as outputted by the device \(J\ m^{-2}\ mm^{-1}\)
Pcum_meas cumulative rainfall amount \(mm\)
Ecum_meas cumulative kinetic energy \(J\ m^{-2}\ mm^{-1}\)
NP number of particles detected (-)
ND particle density \(m^{-3}\ mm^{-1}\)
R rainfall intensity \(mm\ h^{-1}\)
P rainfall amount \(mm\)
Z radar reflectivity \(dB\ mm^6\ m^{-3}\)
M water content \(g m^{-3}\)
E kinetic energy \(J\ m^{-2}\ mm^{-1}\)
Pcum cumulative rainfall amount \(mm\)
Ecum cumulative kinetic energy \(J\ m^{-2}\ mm^{-1}\)
D10 drop diameter’s 10th percentile \(mm\)
D25 drop diameter’s 25th percentile \(mm\)
D50 drop diameter’s 50th percentile \(mm\)
D75 drop diameter’s 75th percentile \(mm\)
D90 drop diameter’s 90th percentile \(mm\)
Dm mean drop diameter \(mm\)
V10 drop velocity’s 10th percentile \(m\ s^{-1}\)
V25 drop velocity’s 25th percentile \(m\ s^{-1}\)
V50 drop velocity’s 50th percentile \(m\ s^{-1}\)
V75 drop velocity’s 75th percentile \(m\ s^{-1}\)
V90 drop velocity’s 90th percentile \(m\ s^{-1}\)
Vm mean drop velocity \(m\ s^{-1}\)

2 Exploratory analysis

With the objective of comparing the behaviour of the two disdrometer types for several variables, we use different plotting tools for a first, exploratory, analysis. Different colors and linetypes will be used to discriminate between measuring devices.

2.1 Cumulative variables

Time series of cumulative precipitation and kinetic energy over the whole experiment. The internally computed values (measured) are compared to those calculated from the PSVD (calculated). We will produce plots for both filtered and unfiltered data.

Filtered data

Unfiltered data

2.2 Density plots, all minutes

We will now have a look at the kernel densities of the integrated variables. All the minute records will be included in the plot.

Filtered data

Unfiltered data

2.3 Violin plots

The same, but with violin plots (might be easier to read to some),

Filtered data

Unfiltered data

2.4 Density plots, by intensity ranges

We will repeat now the kernel density plots, but discriminating between low, medium and high precipitation intensity.

0.1 mm/h < R < 2 mm/h; N = 52306

2 mm/h < R < 10 mm/h; N = 6954

R > 10 mm/h; N = 1377

2.5 Density plots, events

We will now make density plots as the previous ones, but for events (and not minutes).


3 Analysis

We will use a Gamma Generalized Linear Mixed-Effects Model to compare between the two disdrometer types, with the factor Type as fixed effect and the factor Mast as random variable. For several dependet variables (ND, R, E) we use a log link, while we use an identity link for the rest (Z, D10, D50, etc).

3.1 Minute data, all intensities

# take a random sample of 250 complete minutes x 4 devices = 1000
set.seed(12345)
smp <- names(which(table(as.character(dat$Time))==4))
smp <- sample(smp, 250) # times 4 = 1000 records
smp <- which(dat$Time %in% smp)

m_np <- glmer(NP ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_np)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: NP ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  12597.1  12616.7  -6294.6  12589.1      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.0821 -0.6786 -0.2859  0.3537  7.1889 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.0000   0.0000  
##  Residual             0.7602   0.8719  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  5.26687    0.03494   150.7   <2e-16 ***
## TypeThi  5.43832    0.03494   155.6   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_np)$coeff[,1]),4)
## TypePar TypeThi 
##   193.8   230.1
m_d10 <- glmer(D10 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d10)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D10 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  -2682.4  -2662.8   1345.2  -2690.4      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2831 -0.6322 -0.1682  0.3860  7.6834 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 1.306e-05 0.003614
##  Residual             2.993e-02 0.173013
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 0.477206   0.005418   88.08   <2e-16 ***
## TypeThi 0.337419   0.004865   69.36   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.682
signif(summary(m_d10)$coeff[,1],4)
## TypePar TypeThi 
##  0.4772  0.3374
m_d50 <- glmer(D50 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d50)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D50 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  -1424.3  -1404.7    716.2  -1432.3      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.6106 -0.6264 -0.0944  0.4341  6.9348 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 2.215e-06 0.001488
##  Residual             3.607e-02 0.189923
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 0.742047   0.006127   121.1   <2e-16 ***
## TypeThi 0.595601   0.004990   119.4   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.066
signif(summary(m_d50)$coeff[,1],4)
## TypePar TypeThi 
##  0.7420  0.5956
m_d90 <- glmer(D90 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d90)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D90 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   -374.0   -354.4    191.0   -382.0      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.4395 -0.7197 -0.1848  0.5361  5.1552 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.0000  
##  Residual             0.04363  0.2089  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 1.025600   0.009111   112.6   <2e-16 ***
## TypeThi 1.011874   0.008989   112.6   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_d90)$coeff[,1],4)
## TypePar TypeThi 
##   1.026   1.012
m_v10 <- glmer(V10 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v10)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V10 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    464.6    484.2   -228.3    456.6      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.5246 -0.6805 -0.1931  0.5112  6.2395 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0002945 0.01716 
##  Residual             0.0439691 0.20969 
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  1.79271    0.02637   67.99   <2e-16 ***
## TypeThi  1.31562    0.02401   54.80   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.691
signif(summary(m_v10)$coeff[,1],4)
## TypePar TypeThi 
##   1.793   1.316
m_v50 <- glmer(V50 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v50)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V50 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   1127.6   1147.2   -559.8   1119.6      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9613 -0.6035 -0.0436  0.4903  4.7745 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0006002 0.0245  
##  Residual             0.0270815 0.1646  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  2.87503    0.03803   75.59   <2e-16 ***
## TypeThi  2.39933    0.03625   66.18   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.733
signif(summary(m_v50)$coeff[,1],4)
## TypePar TypeThi 
##   2.875   2.399
m_v90 <- glmer(V90 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v90)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V90 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   1520.7   1540.3   -756.4   1512.7      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.8928 -0.6610 -0.1318  0.4945  5.4572 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.000144 0.0120  
##  Residual             0.020889 0.1445  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  3.60780    0.02563   140.8   <2e-16 ***
## TypeThi  3.81758    0.02679   142.5   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.217
signif(summary(m_v90)$coeff[,1],4)
## TypePar TypeThi 
##   3.608   3.818
m_nd <- glmer(ND ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_nd)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: ND ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  21215.0  21234.6 -10603.5  21207.0      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6431 -0.7528 -0.2152  0.5783  3.4818 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.000    0.000   
##  Residual             0.334    0.578   
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  9.67556    0.02666   362.9   <2e-16 ***
## TypeThi  9.98055    0.02666   374.3   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_nd)$coeff[,1]),4)
## TypePar TypeThi 
##   15920   21600
m_r <- glmer(R ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_r)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: R ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   2611.0   2630.7  -1301.5   2603.0      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -0.6338 -0.4918 -0.3096  0.0853 11.2450 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 5.252e-16 2.292e-08
##  Residual             2.153e+00 1.467e+00
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  0.22639    0.04325   5.234 1.66e-07 ***
## TypeThi  0.36455    0.04325   8.428  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_r)$coeff[,1]),4)
## TypePar TypeThi 
##   1.254   1.440
m_z <- glmer(Z ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_z)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: Z ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   6629.8   6649.5  -3310.9   6621.8      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1169 -0.7365 -0.0692  0.6558  4.6984 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.0000  
##  Residual             0.07999  0.2828  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  3.14564    0.01275   246.7   <2e-16 ***
## TypeThi  3.20075    0.01275   251.0   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_z)$coeff[,1]),4)
## TypePar TypeThi 
##   23.23   24.55
m_e <- glmer(E ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_e)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: E ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   5718.0   5737.7  -2855.0   5710.0      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.3507 -0.6936 -0.2482  0.3910  6.4739 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 4.406e-16 2.099e-08
##  Residual             2.413e-01 4.912e-01
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  2.26802    0.01936   117.1   <2e-16 ***
## TypeThi  2.40603    0.01936   124.3   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_e)$coeff[,1]),4)
## TypePar TypeThi 
##    9.66   11.09
# pars <- rbind(c(summary(m_r)$co[c(1,2),1],summary(m_r)$co[1,2]),
#               c(summary(m_e)$co[c(1,2),1],summary(m_e)$co[1,2]))
# rownames(pars) <- c('r','e')
# kable(pars, digits=4,
#       col.names=c('Parsivel','Thies','st. error'))

3.2 Minute data, low intensities

set.seed(12345)
w <- dat$R>0.1 & dat$R<2
smp <- names(which(table(as.character(dat$Time[w]))==4))
smp <- sample(smp, 250)
smp <- which(dat$Time %in% smp)

m_np <- glmer(NP ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_np)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: NP ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  11611.7  11631.4  -5801.9  11603.7      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.2872 -0.6908 -0.2998  0.4176  5.5360 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 1.282e-14 1.132e-07
##  Residual             5.082e-01 7.129e-01
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  4.91330    0.02991   164.3   <2e-16 ***
## TypeThi  4.98192    0.02991   166.6   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_np)$coeff[,1]),4)
## TypePar TypeThi 
##   136.1   145.8
m_d10 <- glmer(D10 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d10)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D10 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  -2631.5  -2611.9   1319.8  -2639.5      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3397 -0.6646 -0.1859  0.3413  5.9460 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 1.594e-05 0.003992
##  Residual             2.939e-02 0.171445
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 0.474142   0.006038   78.52   <2e-16 ***
## TypeThi 0.346188   0.005572   62.13   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.739
signif(summary(m_d10)$coeff[,1],4)
## TypePar TypeThi 
##  0.4741  0.3462
m_d50 <- glmer(D50 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d50)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D50 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  -1758.7  -1739.0    883.3  -1766.7      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.6658 -0.5949 -0.1181  0.4507  7.3972 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 1.89e-05 0.004348
##  Residual             2.65e-02 0.162801
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 0.711337   0.006915  102.88   <2e-16 ***
## TypeThi 0.596354   0.006374   93.56   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.536
signif(summary(m_d50)$coeff[,1],4)
## TypePar TypeThi 
##  0.7113  0.5964
m_d90 <- glmer(D90 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d90)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D90 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  -1048.6  -1029.0    528.3  -1056.6      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1166 -0.7311 -0.1326  0.5222  6.3904 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.0000  
##  Residual             0.02441  0.1562  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 0.956236   0.006453   148.2   <2e-16 ***
## TypeThi 0.947202   0.006392   148.2   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_d90)$coeff[,1],4)
## TypePar TypeThi 
##  0.9562  0.9472
m_v10 <- glmer(V10 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v10)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V10 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    566.7    586.3   -279.3    558.7      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1238 -0.6849 -0.1753  0.4909  5.3177 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0004318 0.02078 
##  Residual             0.0473658 0.21764 
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  1.79182    0.03143   57.02   <2e-16 ***
## TypeThi  1.35611    0.02948   46.00   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.767
signif(summary(m_v10)$coeff[,1],4)
## TypePar TypeThi 
##   1.792   1.356
m_v50 <- glmer(V50 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v50)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V50 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    902.5    922.1   -447.3    894.5      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2335 -0.6208 -0.0640  0.4951  4.8059 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0006181 0.02486 
##  Residual             0.0222395 0.14913 
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  2.79649    0.03875   72.17   <2e-16 ***
## TypeThi  2.40451    0.03760   63.95   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.800
signif(summary(m_v50)$coeff[,1],4)
## TypePar TypeThi 
##   2.796   2.405
m_v90 <- glmer(V90 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v90)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V90 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    912.3    932.0   -452.2    904.3      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.8084 -0.6630 -0.0925  0.5484  6.3241 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0002455 0.01567 
##  Residual             0.0118714 0.10896 
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  3.45799    0.02462   140.5   <2e-16 ***
## TypeThi  3.65312    0.02526   144.6   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.532
signif(summary(m_v90)$coeff[,1],4)
## TypePar TypeThi 
##   3.458   3.653
m_r <- glmer(R ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_r)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: R ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    832.1    851.8   -412.1    824.1      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.2226 -0.8130 -0.3133  0.5859  3.2387 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.0000   0.0000  
##  Residual             0.4785   0.6917  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar -0.49609    0.03022  -16.42   <2e-16 ***
## TypeThi -0.40135    0.03022  -13.28   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_r)$coeff[,1]),4)
## TypePar TypeThi 
##  0.6089  0.6694
m_nd <- glmer(ND ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_nd)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: ND ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  21246.3  21265.9 -10619.1  21238.3      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.8728 -0.7468 -0.1666  0.6511  4.1239 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 5.026e-15 7.090e-08
##  Residual             2.564e-01 5.064e-01
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  9.79288    0.02398   408.5   <2e-16 ***
## TypeThi 10.05533    0.02398   419.4   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_nd)$coeff[,1]),4)
## TypePar TypeThi 
##   17910   23280
m_z <- glmer(Z ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_z)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: Z ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   6090.3   6110.0  -3041.2   6082.3      996 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.41988 -0.78343 -0.04816  0.75447  2.65707 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.0000  
##  Residual             0.05775  0.2403  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  3.01534    0.01098   274.7   <2e-16 ***
## TypeThi  3.07694    0.01098   280.3   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_z)$coeff[,1]),4)
## TypePar TypeThi 
##   20.40   21.69
m_e <- glmer(E ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_e)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: E ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   5251.7   5271.4  -2621.9   5243.7      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.3577 -0.7019 -0.2914  0.4453  7.9470 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 7.157e-05 0.00846 
##  Residual             1.995e-01 0.44671 
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  2.10533    0.01891   111.3   <2e-16 ***
## TypeThi  2.28675    0.01891   120.9   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.150
signif(exp(summary(m_e)$coeff[,1]),4)
## TypePar TypeThi 
##   8.210   9.843

3.3 Minute data, medium intensities

set.seed(12345)
w <- dat$R>2 & dat$R<10
smp <- names(which(table(as.character(dat$Time[w]))==4))
smp <- sample(smp, 250)
smp <- which(dat$Time %in% smp)

m_np <- glmer(NP ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_np)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: NP ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  13197.5  13217.1  -6594.7  13189.5      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1618 -0.6774 -0.1187  0.5470  4.4012 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 9.887e-18 3.144e-09
##  Residual             1.611e-01 4.014e-01
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  6.01151    0.01818   330.7   <2e-16 ***
## TypeThi  6.25221    0.01818   343.9   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_np)$coeff[,1]),4)
## TypePar TypeThi 
##   408.1   519.2
m_d10 <- glmer(D10 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d10)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D10 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  -3048.5  -3028.9   1528.3  -3056.5      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.6541 -0.5325 -0.2016  0.3660  8.7598 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 9.193e-07 0.0009588
##  Residual             1.988e-02 0.1410025
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 0.499927   0.003135   159.4   <2e-16 ***
## TypeThi 0.311117   0.002086   149.2   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.135
signif(summary(m_d10)$coeff[,1],4)
## TypePar TypeThi 
##  0.4999  0.3111
m_d50 <- glmer(D50 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d50)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D50 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  -1410.3  -1390.6    709.1  -1418.3      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.5283 -0.5522 -0.0745  0.5393  6.0584 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 2.666e-19 5.163e-10
##  Residual             3.057e-02 1.748e-01
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 0.835236   0.006410   130.3   <2e-16 ***
## TypeThi 0.586644   0.004502   130.3   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_d50)$coeff[,1],4)
## TypePar TypeThi 
##  0.8352  0.5866
m_d90 <- glmer(D90 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d90)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D90 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   -764.4   -744.8    386.2   -772.4      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3493 -0.6430 -0.1135  0.5268  5.4199 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 3.219e-05 0.005673
##  Residual             1.790e-02 0.133799
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 1.289742   0.009674   133.3   <2e-16 ***
## TypeThi 1.262245   0.009551   132.2   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.409
signif(summary(m_d90)$coeff[,1],4)
## TypePar TypeThi 
##   1.290   1.262
m_v10 <- glmer(V10 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v10)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V10 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    126.1    145.7    -59.0    118.1      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.7366 -0.5881 -0.1272  0.4745  5.0423 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 8.311e-05 0.009116
##  Residual             3.081e-02 0.175517
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  1.91711    0.01802  106.38   <2e-16 ***
## TypeThi  1.16826    0.01366   85.55   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.425
signif(summary(m_v10)$coeff[,1],4)
## TypePar TypeThi 
##   1.917   1.168
m_v50 <- glmer(V50 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v50)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V50 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   1302.1   1321.8   -647.1   1294.1      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0899 -0.4481  0.0094  0.4225  3.8752 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0005477 0.0234  
##  Residual             0.0276997 0.1664  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  3.16341    0.03854   82.08   <2e-16 ***
## TypeThi  2.38821    0.03519   67.87   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.672
signif(summary(m_v50)$coeff[,1],4)
## TypePar TypeThi 
##   3.163   2.388
m_v90 <- glmer(V90 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v90)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V90 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   1137.4   1157.0   -564.7   1129.4      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.7301 -0.6187 -0.1094  0.4792  6.0437 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0008789 0.02965 
##  Residual             0.0105450 0.10269 
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  4.16510    0.04485   92.87   <2e-16 ***
## TypeThi  4.48776    0.04545   98.74   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.822
signif(summary(m_v90)$coeff[,1],4)
## TypePar TypeThi 
##   4.165   4.488
m_r <- glmer(R ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_r)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: R ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   3350.0   3369.6  -1671.0   3342.0      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.2973 -0.7496 -0.3104  0.4944  3.6479 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0004825 0.02197 
##  Residual             0.1498136 0.38706 
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  1.24730    0.02908   42.90   <2e-16 ***
## TypeThi  1.40275    0.02908   48.23   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.700
signif(exp(summary(m_r)$coeff[,1]),4)
## TypePar TypeThi 
##   3.481   4.066
m_nd <- glmer(ND ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_nd)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: ND ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  19557.2  19576.9  -9774.6  19549.2      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2685 -0.6657 -0.0538  0.5041  4.7304 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0003262 0.01806 
##  Residual             0.1686467 0.41067 
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  8.99852    0.02821   319.0   <2e-16 ***
## TypeThi  9.51987    0.02822   337.3   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.532
signif(exp(summary(m_nd)$coeff[,1]),4)
## TypePar TypeThi 
##    8091   13630
m_z <- glmer(Z ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_z)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: Z ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   5300.8   5320.5  -2646.4   5292.8      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3300 -0.6868 -0.0350  0.6187  6.2366 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 6.607e-05 0.008128
##  Residual             1.070e-02 0.103450
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  3.47242    0.01343   258.5   <2e-16 ***
## TypeThi  3.54035    0.01343   263.5   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.884
signif(exp(summary(m_z)$coeff[,1]),4)
## TypePar TypeThi 
##   32.21   34.48
m_e <- glmer(E ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_e)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: E ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   5989.7   6009.3  -2990.8   5981.7      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.7965 -0.6786 -0.1749  0.4920  7.3097 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0002245 0.01498 
##  Residual             0.1337879 0.36577 
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  2.65701    0.02166   122.7   <2e-16 ***
## TypeThi  2.72613    0.02165   125.9   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.510
signif(exp(summary(m_e)$coeff[,1]),4)
## TypePar TypeThi 
##   14.25   15.27

3.4 Minute data, high intensities

set.seed(12345)
w <- dat$R>10
smp <- names(which(table(as.character(dat$Time[w]))==4))
#smp <- sample(smp, 250)
smp <- which(dat$Time %in% smp)

m_np <- glmer(NP ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_np)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: NP ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   2062.0   2073.8  -1027.0   2054.0      136 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.79405 -0.70194 -0.07279  0.70325  2.79076 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 8.581e-17 9.263e-09
##  Residual             1.247e-01 3.532e-01
## Number of obs: 140, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  6.72105    0.04327   155.3   <2e-16 ***
## TypeThi  7.22026    0.04327   166.9   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_np)$coeff[,1]),4)
## TypePar TypeThi 
##   829.7  1367.0
m_d10 <- glmer(D10 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d10)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D10 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   -322.4   -310.7    165.2   -330.4      136 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2763 -0.3532 -0.0961  0.2916  4.3168 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.0000  
##  Residual             0.03624  0.1904  
## Number of obs: 140, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 0.541771   0.012262   44.18   <2e-16 ***
## TypeThi 0.287257   0.006502   44.18   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_d10)$coeff[,1],4)
## TypePar TypeThi 
##  0.5418  0.2873
m_d50 <- glmer(D50 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d50)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D50 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    -53.8    -42.0     30.9    -61.8      136 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.8435 -0.6324 -0.1969  0.5777  4.3107 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.0000  
##  Residual             0.08057  0.2839  
## Number of obs: 140, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  1.02159    0.03329   30.68   <2e-16 ***
## TypeThi  0.51403    0.01675   30.68   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_d50)$coeff[,1],4)
## TypePar TypeThi 
##   1.022   0.514
m_d90 <- glmer(D90 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_d90)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D90 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##      4.7     16.4      1.7     -3.3      136 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.8891 -0.5761  0.0475  0.6547  2.0580 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0003012 0.01735 
##  Residual             0.0192539 0.13876 
## Number of obs: 140, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  1.75368    0.03625   48.38   <2e-16 ***
## TypeThi  1.54184    0.03323   46.40   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.323
signif(summary(m_d90)$coeff[,1],4)
## TypePar TypeThi 
##   1.754   1.542
m_v10 <- glmer(V10 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v10)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V10 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##     93.9    105.7    -43.0     85.9      136 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3019 -0.3373 -0.0704  0.3722  3.2634 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.000   
##  Residual             0.05018  0.224   
## Number of obs: 140, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  2.05021    0.05654   36.26   <2e-16 ***
## TypeThi  1.01251    0.02792   36.26   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_v10)$coeff[,1],4)
## TypePar TypeThi 
##   2.050   1.013
m_v50 <- glmer(V50 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v50)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V50 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    303.6    315.4   -147.8    295.6      136 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.8863 -0.6943 -0.1595  0.5437  3.3335 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 3.003e-15 5.48e-08
##  Residual             7.509e-02 2.74e-01
## Number of obs: 140, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  3.51254    0.11130   31.56   <2e-16 ***
## TypeThi  2.02566    0.06419   31.56   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_v50)$coeff[,1],4)
## TypePar TypeThi 
##   3.513   2.026
m_v90 <- glmer(V90 ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='identity'))
summary(m_v90)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V90 ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    251.0    262.8   -121.5    243.0      136 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.7136 -0.5556  0.1160  0.7763  2.3175 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.0000  
##  Residual             0.01136  0.1066  
## Number of obs: 140, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  5.42417    0.07127    76.1   <2e-16 ***
## TypeThi  5.03647    0.06618    76.1   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_v90)$coeff[,1],4)
## TypePar TypeThi 
##   5.424   5.036
m_r <- glmer(R ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_r)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: R ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    794.0    805.8   -393.0    786.0      136 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.1622 -0.7134 -0.2855  0.3048  3.7446 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0006211 0.02492 
##  Residual             0.0824078 0.28707 
## Number of obs: 140, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  2.67881    0.04016   66.70   <2e-16 ***
## TypeThi  2.79071    0.04018   69.45   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.385
signif(exp(summary(m_r)$coeff[,1]),4)
## TypePar TypeThi 
##   14.57   16.29
m_nd <- glmer(ND ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_nd)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: ND ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   2593.9   2605.7  -1293.0   2585.9      136 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.8497 -0.7144 -0.1017  0.6164  2.9441 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.0000   0.000   
##  Residual             0.1772   0.421   
## Number of obs: 140, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  8.19551    0.05125   159.9   <2e-16 ***
## TypeThi  9.24373    0.05125   180.4   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_nd)$coeff[,1]),4)
## TypePar TypeThi 
##    3625   10340
m_z <- glmer(Z ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_z)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: Z ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    780.4    792.2   -386.2    772.4      136 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6260 -0.7544 -0.1384  0.6452  3.4314 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0001039 0.01019 
##  Residual             0.0083872 0.09158 
## Number of obs: 140, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  3.71113    0.01608   230.8   <2e-16 ***
## TypeThi  3.76472    0.01608   234.1   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.552
signif(exp(summary(m_z)$coeff[,1]),4)
## TypePar TypeThi 
##   40.90   43.15
m_e <- glmer(E ~ 0 + Type + (1|Mast), data=dat[smp,], Gamma(link='log'))
summary(m_e)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: E ~ 0 + Type + (1 | Mast)
##    Data: dat[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    921.7    933.5   -456.9    913.7      136 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.67339 -0.78135 -0.02104  0.72178  2.41577 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.0000   0.0000  
##  Residual             0.1005   0.3169  
## Number of obs: 140, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  3.02246    0.03853   78.44   <2e-16 ***
## TypeThi  2.98655    0.03853   77.51   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_e)$coeff[,1]),4)
## TypePar TypeThi 
##   20.54   19.82

3.5 Event data

set.seed(12345)
smp <- names(which(table(as.character(events$ev))==4))
smp <- which(events$ev %in% smp)

events$Type <- as.factor(substr(events$ID, 1, 1))
events$Mast <- as.factor(substr(events$ID, 2, 2))

m_np <- glmer(NPm ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='log'))
summary(m_np)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: NPm ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   7445.9   7463.7  -3719.0   7437.9      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.0900 -0.6855 -0.2911  0.4095  6.4404 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.0000   0.0000  
##  Residual             0.7162   0.8463  
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP  4.98561    0.04127   120.8   <2e-16 ***
## TypeT  5.12095    0.04127   124.1   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.000
signif(exp(summary(m_np)$coeff[,1]),4)
## TypeP TypeT 
## 146.3 167.5
m_d10m <- glmer(D10m ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='identity'))
summary(m_d10m)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D10m ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  -1703.6  -1685.9    855.8  -1711.6      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2966 -0.5831 -0.1623  0.2727  7.1333 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 9.440e-06 0.003073
##  Residual             2.653e-02 0.162887
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP 0.490417   0.005284   92.82   <2e-16 ***
## TypeT 0.344783   0.004375   78.81   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.457
signif(summary(m_d10m)$coeff[,1],4)
##  TypeP  TypeT 
## 0.4904 0.3448
m_d50m <- glmer(D50m ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='identity'))
summary(m_d50m)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D50m ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  -1094.1  -1076.3    551.0  -1102.1      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2411 -0.5889 -0.1982  0.4353  5.1513 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.0000  
##  Residual             0.02446  0.1564  
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP 0.755960   0.006363   118.8   <2e-16 ***
## TypeT 0.606134   0.005102   118.8   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.000
signif(summary(m_d50m)$coeff[,1],4)
##  TypeP  TypeT 
## 0.7560 0.6061
m_d90m <- glmer(D90m ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='identity'))
summary(m_d90m)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D90m ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   -573.2   -555.4    290.6   -581.2      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1091 -0.6793 -0.1957  0.5421  4.3635 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.0000  
##  Residual             0.02453  0.1566  
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP 1.027353   0.008781     117   <2e-16 ***
## TypeT 0.997098   0.008522     117   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.000
signif(summary(m_d90m)$coeff[,1],4)
##  TypeP  TypeT 
## 1.0270 0.9971
m_v10 <- glmer(V10m ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='identity'))
summary(m_v10)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V10m ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    246.6    264.3   -119.3    238.6      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9823 -0.5803 -0.1328  0.3729  7.5876 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0004109 0.02027 
##  Residual             0.0414589 0.20361 
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP  1.82617    0.03047   59.94   <2e-16 ***
## TypeT  1.35088    0.02751   49.10   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.656
signif(summary(m_v10)$coeff[,1],4)
## TypeP TypeT 
## 1.826 1.351
m_v50m <- glmer(V50m ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='identity'))
summary(m_v50m)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V50m ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    490.1    507.8   -241.0    482.1      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.8147 -0.6161 -0.1298  0.4716  4.0429 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0006798 0.02607 
##  Residual             0.0189075 0.13750 
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP  2.87634    0.04004   71.83   <2e-16 ***
## TypeT  2.46546    0.03843   64.16   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.732
signif(summary(m_v50m)$coeff[,1],4)
## TypeP TypeT 
## 2.876 2.465
m_v90m <- glmer(V90m ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='identity'))
summary(m_v90m)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V90m ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    641.5    659.2   -316.7    633.5      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.4097 -0.6501 -0.1493  0.5465  4.4468 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0003638 0.01907 
##  Residual             0.0124082 0.11139 
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP  3.59669    0.03087   116.5   <2e-16 ***
## TypeT  3.79053    0.03174   119.4   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.469
signif(summary(m_v90m)$coeff[,1],4)
## TypeP TypeT 
## 3.597 3.791
m_rm <- glmer(Rm ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='identity'))
summary(m_rm)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: Rm ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   1213.5   1231.2   -602.8   1205.5      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -0.8291 -0.6023 -0.3136  0.1326  6.8324 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.000    0.000   
##  Residual             1.152    1.073   
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP  0.96152    0.04431    21.7   <2e-16 ***
## TypeT  1.05067    0.04842    21.7   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.000
signif(summary(m_rm)$coeff[,1],4)
##  TypeP  TypeT 
## 0.9615 1.0510
m_rmx <- glmer(RM ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='identity'))
summary(m_rmx)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: RM ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   2769.6   2787.4  -1380.8   2761.6      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -0.6106 -0.5117 -0.3353  0.0196  7.6037 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 4.607e-15 6.788e-08
##  Residual             2.508e+00 1.584e+00
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP   3.4303     0.2155   15.92   <2e-16 ***
## TypeT   3.3511     0.2105   15.92   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.000
signif(summary(m_rmx)$coeff[,1],4)
## TypeP TypeT 
## 3.430 3.351
m_nd <- glmer(NDm ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='identity'))
summary(m_nd)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: NDm ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  13049.2  13067.0  -6520.6  13041.2      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9160 -0.7685 -0.0458  0.6451  6.7750 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 8.618e-09 9.283e-05
##  Residual             2.223e-01 4.714e-01
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP 15930.75      24.19   658.6   <2e-16 ***
## TypeT 20775.60      94.53   219.8   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.000
signif(summary(m_nd)$coeff[,1],4)
## TypeP TypeT 
## 15930 20780
m_em <- glmer(Em ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='identity'))
summary(m_em)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: Em ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   3255.4   3273.1  -1623.7   3247.4      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5274 -0.6526 -0.2305  0.3031  7.7509 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 3.485e-14 1.867e-07
##  Residual             1.438e-01 3.792e-01
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP   9.5049     0.1778   53.46   <2e-16 ***
## TypeT  11.0292     0.2063   53.46   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.000
signif(summary(m_em)$coeff[,1],4)
##  TypeP  TypeT 
##  9.505 11.030
m_zm <- glmer(Zm ~ 0 + Type + (1|Mast), data=events[smp,], Gamma(link='identity'))
summary(m_zm)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: Zm ~ 0 + Type + (1 | Mast)
##    Data: events[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   3635.8   3653.5  -1813.9   3627.8      620 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.0056 -0.7468 -0.1406  0.5875  3.9705 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 3.505e-14 1.872e-07
##  Residual             4.277e-02 2.068e-01
## Number of obs: 624, groups:  Mast, 2
## 
## Fixed effects:
##       Estimate Std. Error t value Pr(>|z|)    
## TypeP  21.5480     0.2469   87.26   <2e-16 ***
## TypeT  22.7508     0.2607   87.26   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       TypeP
## TypeT 0.000
signif(summary(m_zm)$coeff[,1],4)
## TypeP TypeT 
## 21.55 22.75

3.6 Un-filtered data

set.seed(12345)
smp <- names(which(table(as.character(datunf$Time))==4))
smp <- sample(smp, 250) # times 4 = 1000 records
smp <- which(datunf$Time %in% smp)

m_np <- glmer(NP_meas ~ 0 + Type + (1|Mast), data=datunf[smp,], Gamma(link='log'))
summary(m_np)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: NP_meas ~ 0 + Type + (1 | Mast)
##    Data: datunf[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  12922.2  12941.9  -6457.1  12914.2      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -0.9206 -0.5996 -0.2839  0.2625 10.4933 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 1.278e-16 1.130e-08
##  Residual             1.055e+00 1.027e+00
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  5.25852    0.03613   145.5   <2e-16 ***
## TypeThi  5.74157    0.03613   158.9   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_np)$coeff[,1]),4)
## TypePar TypeThi 
##   192.2   311.6
m_r <- glmer(R ~ 0 + Type + (1|Mast), data=datunf[smp,], Gamma(link='log'))
summary(m_r)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: R ~ 0 + Type + (1 | Mast)
##    Data: datunf[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   2471.5   2491.1  -1231.8   2463.5      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -0.5568 -0.4384 -0.2830  0.1104 18.5683 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.000    0.00    
##  Residual             2.756    1.66    
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  0.16806    0.04353   3.861 0.000113 ***
## TypeThi  0.28237    0.04353   6.487 8.77e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_r)$coeff[,1]),4)
## TypePar TypeThi 
##   1.183   1.326
m_nd <- glmer(ND ~ 0 + Type + (1|Mast), data=datunf[smp,], Gamma(link='log'))
summary(m_nd)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: ND ~ 0 + Type + (1 | Mast)
##    Data: datunf[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  21721.8  21741.4 -10856.9  21713.8      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5332 -0.6897 -0.1956  0.4718 13.7462 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 1.554e-14 1.246e-07
##  Residual             3.884e-01 6.232e-01
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar    9.784      0.026   376.3   <2e-16 ***
## TypeThi   10.416      0.026   400.6   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_nd)$coeff[,1]),4)
## TypePar TypeThi 
##   17750   33370
m_z <- glmer(Z ~ 0 + Type + (1|Mast), data=datunf[smp,], Gamma(link='log'))
summary(m_z)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: Z ~ 0 + Type + (1 | Mast)
##    Data: datunf[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   6645.5   6665.2  -3318.8   6637.5      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.0737 -0.7527 -0.0638  0.6854  7.0290 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.0000  
##  Residual             0.08807  0.2968  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  3.11128    0.01326   234.7   <2e-16 ***
## TypeThi  3.17804    0.01326   239.8   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_z)$coeff[,1]),4)
## TypePar TypeThi 
##   22.45   24.00
m_e <- glmer(E ~ 0 + Type + (1|Mast), data=datunf[smp,], Gamma(link='log'))
summary(m_e)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: E ~ 0 + Type + (1 | Mast)
##    Data: datunf[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   5531.3   5550.9  -2761.7   5523.3      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.4706 -0.7400 -0.2485  0.4481  6.2657 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.000    0.0000  
##  Residual             0.224    0.4733  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  2.19362    0.01886   116.3   <2e-16 ***
## TypeThi  2.33900    0.01886   124.0   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(exp(summary(m_e)$coeff[,1]),4)
## TypePar TypeThi 
##   8.968  10.370
m_d10 <- glmer(D10 ~ 0 + Type + (1|Mast), data=datunf[smp,], Gamma(link='identity'))
summary(m_d10)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D10 ~ 0 + Type + (1 | Mast)
##    Data: datunf[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##  -2205.9  -2186.3   1107.0  -2213.9      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.8098 -0.6718 -0.1868  0.4154  4.5570 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  Mast     (Intercept) 7.613e-07 0.0008726
##  Residual             6.217e-02 0.2493323
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 0.500978   0.005314   94.28   <2e-16 ***
## TypeThi 0.240931   0.002656   90.72   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.047
signif(summary(m_d10)$coeff[,1],4)
## TypePar TypeThi 
##  0.5010  0.2409
m_d50 <- glmer(D50 ~ 0 + Type + (1|Mast), data=datunf[smp,], Gamma(link='identity'))
summary(m_d50)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D50 ~ 0 + Type + (1 | Mast)
##    Data: datunf[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   -956.2   -936.6    482.1   -964.2      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2929 -0.6064 -0.0976  0.4887  5.4000 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.000   
##  Residual             0.05856  0.242   
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar 0.803982   0.008372   96.04   <2e-16 ***
## TypeThi 0.530178   0.005521   96.04   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_d50)$coeff[,1],4)
## TypePar TypeThi 
##  0.8040  0.5302
m_d90 <- glmer(D90 ~ 0 + Type + (1|Mast), data=datunf[smp,], Gamma(link='identity'))
summary(m_d90)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: D90 ~ 0 + Type + (1 | Mast)
##    Data: datunf[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    104.5    124.1    -48.3     96.5      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.4958 -0.7027 -0.0964  0.4524  7.5111 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.000   
##  Residual             0.05381  0.232   
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  1.25438    0.01217   103.1   <2e-16 ***
## TypeThi  1.12577    0.01092   103.1   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_d90)$coeff[,1],4)
## TypePar TypeThi 
##   1.254   1.126
m_v10 <- glmer(V10 ~ 0 + Type + (1|Mast), data=datunf[smp,], Gamma(link='identity'))
summary(m_v10)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V10 ~ 0 + Type + (1 | Mast)
##    Data: datunf[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##    796.9    816.6   -394.5    788.9      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1700 -0.7007 -0.0996  0.5290  5.9505 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  Mast     (Intercept) 0.0009373 0.03062 
##  Residual             0.0585776 0.24203 
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  1.97175    0.05085   38.77   <2e-16 ***
## TypeThi  1.19854    0.04806   24.94   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.879
signif(summary(m_v10)$coeff[,1],4)
## TypePar TypeThi 
##   1.972   1.199
m_v50 <- glmer(V50 ~ 0 + Type + (1|Mast), data=datunf[smp,], Gamma(link='identity'))
summary(m_v50)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V50 ~ 0 + Type + (1 | Mast)
##    Data: datunf[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   1318.5   1338.1   -655.3   1310.5      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3737 -0.5433 -0.0580  0.4113  4.9968 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.000   
##  Residual             0.03097  0.176   
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  3.08547    0.02388   129.2   <2e-16 ***
## TypeThi  2.39234    0.01852   129.2   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_v50)$coeff[,1],4)
## TypePar TypeThi 
##   3.085   2.392
m_v90 <- glmer(V90 ~ 0 + Type + (1|Mast), data=datunf[smp,], Gamma(link='identity'))
summary(m_v90)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( identity )
## Formula: V90 ~ 0 + Type + (1 | Mast)
##    Data: datunf[smp, ]
## 
##      AIC      BIC   logLik deviance df.resid 
##   1966.3   1986.0   -979.2   1958.3      996 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9609 -0.7136 -0.1612  0.5034  6.8924 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Mast     (Intercept) 0.00000  0.0000  
##  Residual             0.02694  0.1641  
## Number of obs: 1000, groups:  Mast, 2
## 
## Fixed effects:
##         Estimate Std. Error t value Pr(>|z|)    
## TypePar  4.20303    0.02897   145.1   <2e-16 ***
## TypeThi  4.21452    0.02905   145.1   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         TypePr
## TypeThi 0.000
signif(summary(m_v90)$coeff[,1],4)
## TypePar TypeThi 
##   4.203   4.215

We shall finally try fiting a heteroskedastic model, using glmmPQL from the MASS package. This function fits a Generalized Linear Mixed Effects Model with multivariate normal random effects, using Penalized Quasi-Likelihood.

# IT DOES NOT WORK
#library(nlme)
#library(MASS)
#glmmPQL(d50~0+Type, random=~1|Mast, family=Gamma(link='identity'),
#  data=dat[smp,], weights=varIdent(form=~1|Type))